(a) Under what conditions on the constant k will the function f (x,y) = kx2 − 2xy +...

(a) Under what conditions on the constant k will the function

f (x,y) = kx² − 2xy + ky²

have a nondegenerate local minimum at (0,0)? What about a local maximum?

(b) Under what conditions on the constant k will the function

have a nondegenerate local maximum at (0,0,0)? What about a nondegenerate local minimum?